Consistency of Heyting arithmetic in natural deduction

✍ Scribed by Annika Kanckos

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 153 KB
• Volume: 56
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200910118

✦ Synopsis

Abstract

A proof of the consistency of Heyting arithmetic formulated in natural deduction is given. The proof is a reduction procedure for derivations of falsity and a vector assignment, such that each reduction reduces the vector. By an interpretation of the expressions of the vectors as ordinals each derivation of falsity is assigned an ordinal less than ε 0, thus proving termination of the procedure (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)